How does one make a chess engine play on a live chess website?

http://en.wikipedia.org/wiki/Chess_Engine_Communication_Protocol is commonly used by chess user interfaces and ICS-compatible online chess servers (such as http://www.freechess.org) to communicate with chess engines. Most well known chess engines available on the internet can also communicate using this protocol. To hook up a chess engine with a chess server, you'll have to find a suitable tool (or script one up yourself). For ICS-compatible chess servers, http://www.tim-mann.org/zippy.html is a nice interfacing tool, used by most legitimate online chess engines, such as the ones that play on FICS. Building your own chess engine is however not a trivial task. You can find excellent resources online (http://chessprogramming.wikispaces.com/) to get you started, but you don't need to develop your own chess engine if your goal is simply to hook it up with a chess server, as you could quite easily download an existing engine and interface it with the chess server.